Hypothesis tests Kruskal-Wallis test

These data were compared with the actual data by application of the statistic Kruskal hypothesis test (Kruskal Wallis, 1952) under the null hypothesis that the data follow the same distribution. Three tests were realized for each type of accident (i) test on time to accident, (ii) test on time to recovery and (iii) test on unavailability, amounting six (6) hypothesis tests. Table 2 shows the /7-values of each test. 

Having calculated the level of significance can be obtained from appropriate tables. The Wilcoxon signed rank test is the non-parametric equivalent of the paired t-test. The Kruskal-Wallis test is another rank sums test that is used to test the null hypothesis that k independent samples come from identical populations against the alternative that the means of the populations are unequal. It provides a non-parametric alternative to the one-way analysis of variance. 

There are times when the required assumptions for ANOVA, a parametric test, are not met. One example would be if the underlying distributions are non-normal. In these cases, nonparametric tests are very useful and informative. For example, we saw in Section 11.3 that a nonparametric analog to the two-sample ttest, Wilcoxon s rank sum test, makes use of the ranks of observations rather than the scores themselves. When a one-factor ANOVA is not appropriate in a particular case a corresponding nonparametric approach called the Kruskal-Wallis test can be used. This test is a hypothesis test of the location of (more than) two distributions. 

Kruskal-Wallis test is the technique tests the null hypothesis that several populations have the same median. It is the nonparametric equivalent of the one-factor ANOVA. The test statistic is ... 

The Kruskal-Wallis test is a non-parametric test that compares three or more independent groups, and does not need to assume that the sources come from a normal distribution. It is robust for groups with different sample sizes, and can work with ordinal data (rating-scale data). The nuU hypothesis for this test is that there is no significant difference among the medians of the k-groups . A small p-value rejects the null hypothesis, which means that at least one group s median differs from one of the others. 

To further identify which group is different, a Dunn s post-test is performed. This test compares the difference in the median for each group pair. If the statistic of the pair is greater than the critical value, then the null hypothesis that there is no significant difference between the medians of the pair is rejected. With smaller sample sizes the power of the Kruskal-Wallis test decreases, so these results need to be analyzed carefully. 

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